Page:Lectures on Ten British Physicists of the Nineteenth Century.djvu/46

Tait's Quaternion project had now developed into a formal introduction to Quaternions; an announcement of the forthcoming book appeared soon after Tait removed to Edinburgh. He had now ceased to teach pure mathematics; he and Prof. William Thomson had sketched out an elaborate treatise on natural philosophy in four volumes'; for which reasons he was anxious to have the Quaternion volume off his hands. Sir William Hamilton was then engaged in the preparation of his "Elements of Quaternions" and he did not like the idea of Tait's book appearing before his own. He did not object to examples, but he wished to have the priority in all matters of principle. Tait, hearing of the situation, offered of his own accord to delay the publication of his volume until the Hamilton's Elements should have appeared. To arrange the matter more definitely Tait made a visit to Dunsink Observatory, Dublin, in the summer of 1861. Hamilton expected to publish before the end of the year, and asked Tait to wait till the year following. But the printing of Hamilton's book went on for four years longer, and was stopped only by Hamilton's death in 1865. It was published, incomplete, in 1866; and true to his promise Tait did not publish till 1867. The work then given to the public was entitled an Elementary Treatise on Quaternions. The articles which deal with the theory of Quaternions have always presented numerous difficulties to the reader; this phenomenon is explained partly by the history of the volume, and especially by Hamilton's desire that Tait should confine the work to applications. I think it unfortunate that Hamilton adopted such an attitude. It was a mistake to present the method in such tremendous volumes as the Lectures and the Elements; it was a mistake to retard the publication of Tait's volume; it was a mistake to reserve the discussion of principles and of notation. Unfortunately, Tait, in his turn, advised inquirers to leave principles and notation alone and go on to applications, from which it has come about that the method of quaternions, presenting as it does, many points of novelty to the mathematician, has never been adequately discussed; only a few have looked upon it as a very important subject for discussion.